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Rigorous computations for nonlinear partial differential equations

Grant number: 13/50382-7
Support type:Regular Research Grants
Duration: November 01, 2013 - October 31, 2015
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Applied Mathematics
Cooperation agreement: Consortium of Alberta, Laval, Dalhousie and Ottawa (CALDO)
Principal researcher:Marcio Fuzeto Gameiro
Grantee:Marcio Fuzeto Gameiro
Principal researcher abroad: Jean Phillippe Lessard
Institution abroad: Université Laval, Canada
Home Institution: Instituto de Ciências Matemáticas e de Computação (ICMC). Universidade de São Paulo (USP). São Carlos , SP, Brazil
Associated research grant:13/07460-7 - Rigorous computations for PDEs, AP.R

Abstract

The goal of this research project is to understand global properties of PDEs by developing rigorous computational methods to prove existence of periodic orbits, connecting orbits and even chaotic dynamics for PDEs, with the long-term goal of unlocking the secrets hidden within the dynamics of complicated fluid mechanics models such as the Navier-Stokes equations and Rayleigh-Bénard convection. (AU)

Articles published in Agência FAPESP Newsletter about the research grant:
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Scientific publications (4)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
CASTELLI, ROBERTO; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. Rigorous Numerics for ill-posed PDEs: Periodic Orbits in the Boussinesq Equation. Archive for Rational Mechanics and Analysis, v. 228, n. 1, p. 129-157, APR 2018. Web of Science Citations: 5.
FIGUERAS, JORDI-LLUIS; GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; DE LA LLAVE, RAFAEL. A Framework for the Numerical Computation and A Posteriori Verification of Invariant Objects of Evolution Equations. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 2, p. 1070-1088, 2017. Web of Science Citations: 7.
GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE. A Posteriori Verification of Invariant Objects of Evolution Equations: Periodic Orbits in the Kuramoto-Sivashinsky PDE. SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, v. 16, n. 1, p. 687-728, 2017. Web of Science Citations: 7.
GAMEIRO, MARCIO; LESSARD, JEAN-PHILIPPE; RICAUD, YANN. Rigorous numerics for piecewise-smooth systems: A functional analytic approach based on Chebyshev series. Journal of Computational and Applied Mathematics, v. 292, p. 654-673, JAN 15 2016. Web of Science Citations: 3.

Please report errors in scientific publications list by writing to: cdi@fapesp.br.